Experimental study of energy-minimizing point configurations on spheres
Metric Geometry
2011-10-20 v3
Abstract
In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.
Cite
@article{arxiv.math/0611451,
title = {Experimental study of energy-minimizing point configurations on spheres},
author = {Brandon Ballinger and Grigoriy Blekherman and Henry Cohn and Noah Giansiracusa and Elizabeth Kelly and Achill Schuermann},
journal= {arXiv preprint arXiv:math/0611451},
year = {2011}
}
Comments
41 pages, 12 figures, to appear in Experimental Mathematics